Repairing collision damage to vehicle bodies frequently involves pulling on damaged areas with considerable force, thus requiring the frame to be secured against movement while the damaged area is straightened. Traditionally it was the practice to tie down the vehicle frame with chains and hooks, which could result in further damage to the vehicle, depending on the direction and strength of the pulling forces. Modem body straightening techniques have evolved whereby a damaged vehicle is mounted and secured on a vehicle repair rack so that the exact location of various data points on the vehicle can be measured and repaired, and resistance is provided against pulling forces so that integrity of the undamaged parts of the vehicle is maintained. Typically a conventional repair system utilizes a frame rack consisting of a pair of parallel spaced apart tie-down tracks equipped with four clamping tie-down members, at least two on each track, which can be positioned so as to attach to pinch welds, or other parts, at four corners at the base of a vehicle. It is important that the vehicle to be repaired must rest on the attachments, not on its wheels. As for securing the frame, body styles have changed, and so have the pinch welds. Also, some vehicles have no pinch welds, and others have jack mounts along the rocker panels. For a vehicle body repair shop, this has meant investing in an attachment system for each type of vehicle, requiring more storage area as well as higher equipment costs. Further, the known systems are means of securing the frame at four points to parallel tie down tracks which provide external rigidity to the frame in the fore-to-aft direction, but, with two exceptions, no external rigidity laterally. The exceptions, U.S. Pat. No. 6,745,612 to McIlwraith, and U.S. Pat. No. 4,606,216 to Riutta, teach a full-frame rectangular anchoring system with a rectangular support frame resting on small stands. McIlwriath has rotatable clamping assemblies attachable to a vehicle frame, allowing them to be leveled with respect to the support frame. This invention is very complex with many non-standard, custom-made parts and would be very expensive to manufacture and complicated to use. In particular, both inventions fail to take advantage of the stability and strength of the tie-down tracks of a conventional vehicle frame repair rack on a lift, to reduce cost and complexity as well as to supply a sturdier support than the small stands on which the support frame rests. Thus there is a need for an apparatus for securing varying auto body types and sizes to a conventional vehicle frame rack that is simple to use and inexpensive, that adds external lateral rigidity to the longitudinal stability of a vehicle frame rack, so as to counter pulling forces from any direction on a vehicle to be repaired. Additionally, there is a need for a system that is adaptable to various body types with or without pinch welds.